多面體間的關係

Relations Between Polyhedra

許璧薇(Pi-Wei Hsu)

指導教授 ： 張企 ； 全任重

國立清華大學/理學院/數學系/碩士(2014年)

https://doi.org/10.6843/NTHU.2014.00047

摘要

There discuss that relations between polyhedron.
In Chapter 2, we discuss (1) how polyhedron A having some extremal property be inscribed a given polyhedron B, where A and B can be any of the following types of polyhedron: the cube, regular tetrahedron, regular octahedron, regular dodecahedron and regular icosahedron. Then, we discuss (2) how the polyhedron can be regarded as a convex hull of other polyhedrons. Case (1) deals with two comparable polyhedrons and case (2) deals with two incomparable polyhedrons.
In Chapter 3, we discuss how polyhedron A having some extremal property be exscribed outside a given polyhedron B, where A and B can be any of the following types of polyhedron: the cube, regular tetrahedron, regular octahedron, regular dodecahedron and regular icosahedron. Then, we discuss how the polyhedron can be regarded as a convex hull of other polyhedrons.
In Chapter 4, we stress the projection of a rotating cube upon a given polyhedron. Because projecting a cube is easier than projecting.
In Chapter 5, we discuss the intersection of polyhedrons. Here we address the question: How can a polyhedron be expressed as an intersection of several other regular polyhedrons?
In Chapter 6, we constructed 12 animations showing how can a polyhedron be decomposed into disjoint pieces and then be “reassembled” into another polyhedron (with or without an empty spaces enclosed)?

This thesis is to be accompanied with webpage http://m98.nthu.edu.tw/~s9821603/

關鍵字

Inscribed in a given polyhedron ； Escribed outside a given polyhedron ； Projection ； Intersection ； Inside-out

參考文獻

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